Colloidal Quantum Dot Light Emitting Diodes at Telecom Wavelength with 18% Quantum Efficiency and Over 1 MHz Bandwidth

Abstract Developing high performance, low‐cost solid‐state light emitters in the telecom wavelength bandwidth is of paramount importance for infrared light‐based communications. Colloidal quantum dot (CQD) based light emitting diodes (LEDs) have shown tremendous advances in recent times through improvement in synthesis chemistry, surface property, and device structures. Despite the tremendous advancements of CQD based LEDs in the visible range with efficiency reaching theoretical limits, their short‐wave infrared (SWIR) counterparts mainly based on lead chalcogenide CQDs, have shown lower performance (≈8%). Here the authors report on highly efficient SWIR CQD LEDs with a recorded EQE of 11.8% enabled by the use of a binary CQD matrix comprising QD populations of different bandgaps at the emission wavelength of 1550 nm. By further optimizing the optical out‐coupling via the use of a hemispherical lens to reduce optical waveguide loss, the EQE of the LED increased to 18.6%. The CQD LED has an electrical bandwidth of 2 MHz, which motivated them to demonstrate its use in the first SWIR free‐space optical transmission link based entirely on CQD technology (photodetector and light emitter) opening a new window of applications for CQD optoelectronics.

For full electromagnetics simulation, we used Commercial software, Ansys Lumerical Finite Difference Time Domain (FDTD). The full stack LED device was placed a top of a glass substrate. To calculate the transmitted light in the glass side (bottom of the LED structure), a dipole box with random dipole orientation was employed to model the active medium. All layers of LED are assumed to be homogenous medium for which the refractive indices were extracted from ellipsometry measurement. Perfectly matched layers boundary conditions are used at ±y and periodic boundary conditions are used at ±x direction. The field are recorded using frequency-domain filed and located at the bottom of the structure after glass substrate normal to the y-direction. The fraction of transmitted power is calculated based on the transmitted power in monitor divided by total emitted light from the dipole box.

S5: Hemispherical lens attachment to the LED substrate to reduce optical waveguide loss:
The finite thickness of the ITO coated glass substrate, the difference in refractive index between glass and LED materials contribute to optical waveguide loss through all sides of the device. Organic and colloidal quantum dot based visible LEDs based on similar device structure showed remarkable improvement while using hemispherical lens to reduce the optical loss [1,2]. The schematic of the lens attached glass substrate is shown in Fig. S5 (a).

S8. Three-dimensional packing of colloidal quantum dot in binary and mix-matrix mixing and prediction of dot-to-dot hopping probability:
The average diameter of the emitter QDs is 6 nm (estimated from excitonic absorption peak at 0.79 eV).
Considering the QDs are distributed in isotropic way upon mixing as shown in Fig. S5, we can estimate the volume which contain each of the QD in the matrix.
In 7.5% binary mixing, the number of emitters QDs per 1 cm 3 will be 4 × 10 cm -3 The volume of the cube containing each of the emitter QD as shown in Fig. S8 can be calculated as, 1/(4 × 10 )≈ 2 × 10 cm 3 The edge of each cube will be~√2 × 10 ~12 So, the centre-to-centre distance between two emitter QD in the matrix is ~12 . Figure  S8: Schematic of isotropic Emitter QD distribution in matrix; (b) Centre-to-centre distance between two nearest Emitter QDs.
Considering a similar approach for the 900 nm (1.37 eV) excitonic peak based QDs, we can estimate the dot-to-dot distance between the 900 nm dots is 5.8 nm. Thus, the average distance an electron should hop from the 900 nm dot to another 900 nm dot or 1550 nm emitter dot should be around 5.8 nm. Utilizing these data one can estimate the hopping probability of electron transmission.

Hopping Probability:
The hopping probability can be given by the Miller-Abrahams expression [6],

( )
Here, R is the hopping distance, a is the carrier localization, ΔE is the activation energy for the hopping process. kT is the thermal energy.
Hopping probability of electrons from 900 nm QD to 900 nm/1550 nm QD: The average dot-to-dot distance should be taken as the hopping distance which is given by 5.8 nm. The localization length should be the diameter of 900 nm QD (~2.9 nm). The activation energy for this case is 0 eV. Thus, the Hopping probability can be estimated as,

( )
Hopping probability of electrons from 900 nm QD to 700 nm QD: The average dot-to-dot distance should be taken as the hopping distance as given by 2.1 nm. The localization length should be the diameter of 900 nm QD (~2.9 nm). The activation energy for this case should be the conduction band offset between 900 nm and 700 nm QDs (0.15 eV). Thus, the Hopping probability can be estimated as,

( )
One can estimate (P 1 /P 2 ) as exp (3.5). P 1 is around 31 times more probable than P 2 . Thus, in the mix matrix blend, hopping probability from 900 to 900 nm QDs or the emitter QDs are much higher compared to 900 to 700 nm QDs.

S9: Estimating injection efficiency of mixed matrix devices from SCAPS simulation:
The injection efficiency in an LED is defined by the fraction of charges injected participate in the recombination processes. Thus, the injection efficiency ( ) can be expressed as, ( ) Where is the total recombination rate given by, . is the radiative recombination rate, is the trap assisted recombination rate and is the Auger recombination rate [7]. I is the injection current. The injection efficiency was computed by calculating R tot and I and taking their ratio. Figure S9 shows the variation of and injection current as a function of 1.35 eV QD loading in the blended matrix. The injection efficiency shows improvement with low loading (1-10%) and then it starts decreasing with higher 1.35 QD loading in the matrix due to the variation of these parameters. The lowest value is obtained with 70% loading and it starts to grow again up to 100% loading. This variation matches with the obtained device efficiency with 10% loading shows best performance and it goes down with higher loading and 50% loading-based devices showed lower EQE. The injection efficiency linearly proportional with the EQE of the device.

SCAPS simulation:
The binary device structures are considered similar to our previous reports [5,8]. Figure S9 shows the structure used for SCAPS simulations. For blended matrix, we have taken uniform mixing throughout the matrix. The effective medium approximations for homogeneous mixture were considered. In case of blended matrix, for material properties, uniform (0<y<1) option was chosen. The value of y varied from 0.5 to 0.95 to get the results. The parameters used in the simulation are summarised in Table S2.   Figure S11: The electroluminescence signal response as captured in the oscilloscope as a function of applied voltage. The applied frequency for the experiment was fixed at f=500 kHz.